Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws

Milišić, Vuk

doi:10.1090/S0002-9939-03-06961-2

Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws
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Proc. Amer. Math. Soc. 131 (2003), 1727-1737 Request permission

Abstract:

We present some new convergence results for a discrete velocities BGK approximation to an initial boundary value problem for a single hyperbolic conservation law. In this paper we show stability and convergence toward a unique entropy solution in the general $BV$ framework without any restriction either on the data of the limit problem or on the set of velocity of the BGK model.

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